According to legend, archimedes, who was a famous greek mathematician, was given a crown, which was supposed to be made of pure gold but contained some silver alloy, by king hiero ii of sicily. he was asked by the king to prove or disprove his suspicion. (the crown indeed did contain silver). if you were archimedes, how would have determined experimentally whether or not the crown was pure gold?

By computing the crown's density.

Explanation:

Hello,

In this case, considering Archimedes principle, it would be convenient to take the crown and place it into water by using a volumetric cylinder in order to measure out the displaced volume which matches with the volume of the crown. Then, by using a balance, its weight will be measured.

Now, according to the fomula:

The density of the crown will be computed. Afterwards, the computed density will be compared with the theoretical density of gold in order to determine whether the crown is pure gold or not.

Best regards.